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- W2083083841 abstract "We consider two critical spatial branching processes on $mathbb{R}^d$: critical branching Brownian motion, and the Dawson-Watanabe process. A basic feature of these processes is that their ergodic behavior is highly dimension-dependent. It is known that in low dimensions, $d leq 2$, the unique invariant measure with finite intensity is $delta_0$, the unit point mass on the empty state. In high dimensions, $d geq 3$, there is a one-parameter family of nondegenerate invariant measures. We prove here that for $d leq 2, delta_0$ is the only invariant measure. In our proof we make use of sub- and super-solutions of the partial differential equation $partial u/partial t = (1/2) Delta u - bu^2$." @default.
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- W2083083841 date "1993-10-01" @default.
- W2083083841 modified "2023-10-10" @default.
- W2083083841 title "Ergodicity of Critical Spatial Branching Processes in Low Dimensions" @default.
- W2083083841 doi "https://doi.org/10.1214/aop/1176989006" @default.
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